Dear sir, I use ss2tf function in matlab. Its output values input to tf2ss function. But the result is not equal to the original input. (A1,B1,C1,D1) IS NOT EQUAL TO (A,B,C,D.)
For a given transfer function den.num, there exist infinity possible state space representations. So, ABCD and a1b1c1d1 have the same transfer function. The use of this, is that you can have a lot of different structures that you can implement an will give you the same response. To select between different structures, you should take in account round-off error effects vs speed (i.e. some structures will require more multiplications, but will have better signal to noise ratio - some structures will be more stable than others or less prone to overflow, etc)
If by "no consistent" you mean that tf2ss( ss2tf(x) ) != x, you are right.